A physically consistent framework for microstructural and optical characterization of spinel ferrite nanoparticles:...

This work presents a comparative methodology for assessing the reliability of microstructural and optical parameters derived from different analytical models, using thermally decomposed Mn_0.7Co_0.3Fe₂O₄ nanoparticles as a model system. Fourier-transform infrared spectroscopy confirmed the formation of the spinel ferrite structure, with characteristic tetrahedral and octahedral vibration bands at 550 and 432 cm^-1, respectively. Rietveld refinement established a single-phase cubic spinel structure, while transmission electron microscopy revealed a relatively narrow particle-size distribution with an average diameter of 6.5 nm based on 319 particles. EDX elemental mapping showed a relatively homogeneous spatial distribution of Co, Mn, Fe, and O, with no detectable elemental segregation within the spatial resolution and detection limits of the measurement. To ensure reliable X-ray line-profile analysis, instrumental broadening was calibrated under identical experimental conditions using the certified NIST SRM 660c (LaB₆) standard. Although the Lorentzian and Gaussian limiting assumptions of the Williamson-Hall method produced markedly different microstructural parameters, the Size-Strain Plot and Halder-Wagner methods converged to nearly identical crystallite sizes (∼6.7 nm) with excellent linearity (R² > 0.99). The corresponding microstrain values of (0.58-1.43) × 10^-3 indicate weak lattice distortion, while the close agreement between the TEM particle size and XRD crystallite size suggests predominantly single coherently diffracting domains. Optical analysis yielded band-gap energies of 2.46 and 2.62 eV from the Kubelka-Munk and Kramers-Kronig formalisms, respectively, demonstrating the influence of dispersion effects on diffuse-reflectance analysis. The low Urbach energy (0.047 eV) is consistent with the weak lattice microstrain, indicating a limited degree of both structural and electronic disorder. These results demonstrate that reliable nanoscale parameters depend critically on instrumental calibration and analytical-model selection, highlighting the importance of physically consistent diffraction and optical modeling for the characterization of nanocrystalline spinel ferrites.